Diophantine Equations

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Academic Press, 1969 - 311 頁
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Diophantine Equations
 

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內容

Chapter 1 Introduction
1
Chapter 2 Equations Proved Impossible by Congruence Considerations
3
Chapter 3 Equations Involving Sums of Squares
12
Chapter 4 Quartic Equations with only Trivial Solutions
16
Chapter 5 Some Linear Equations
30
Chapter 6 Properties of Congruences
34
Chapter 7 Homogeneous Equations of the Second Degree
42
Chapter 8 Pells Equation
53
Chapter 18 Representation of Numbers by Homogeneous Forms in Two Variables
157
Chapter 19 Representation of Numbers by Special Binary Quadratic and Quaternary Quadratic Forms
164
Chapter 20 Representation of Numbers by Homogeneous Forms in Several Variables
174
Chapter 21 Representation of Numbers by Polynomials
181
Chapter 22 Thues Theorem on the Integer Solutions of fx y m
186
Chapter 23 Local Methods or pAdic Applications
200
Chapter 24 Binary Cubic Forms
213
Chapter 25 Binary Quartic Forms
232

Chapter 9 Rational Solutions Derived from Given Ones
66
Chapter 10 Rational Points on Some Cubic Curves
76
Chapter 11 Rational Points on Cubic Surfaces
82
Chapter 12 Rational and Integer Points on Quartic Surfaces
90
Chapter 13 Integer Solutions of Some Cubic Equations in Three Variables
100
Chapter 14 Simple Algebraic Considerations
111
Chapter 15 Applications of Algebraic Number Theory
121
Chapter 16 Finite Basis Theorem for the Rational Points on a Cubic Curve fx y z 0 of Genus one
138
Chapter 17 Rational Points on Curves of Genus g 0 or 1 and g 1
150
Chapter 26 The Equation y2 x3 + k
238
Chapter 27 The equation y2 ax3 + bx2 + cx + d
255
Chapter 28 Some Equations of Degree 3
262
Chapter 29 Fermats Last Theorem
280
Chapter 30 Miscellaneous Results
287
Bibiography
306
List of Equations and Congruences
307
Pure and Applied Mathematics
313
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